7. Refractive index of gas (1 weight)
Another useful application of the Michelson interferometer is the measurement of the index
of refraction of a gas by exploiting the relationship between the index of
refraction
n
and
pressure
P
in the gas chamber.
Consider an evacuated cylindrical gas cell, positioned on the viewing axis of mirror A, of
length
l
. Suppose the gas with the index of refraction
n
is admitted into it. The change
in the optical path length will be simply 2
l
(
n
–
1) that gives the exact same relationship as
in the previous sect
ion, for a light of wavelength λ
2
l
(
n
−
1) =
Nλ
,
where N is the number of fringes counted. Take the derivative with respect to pressure:
(6)
It is an experimental fact that for gases the number
n
−
1 is proportional to the density of
the
gas
ρ
, as long as the chemical composition of the gas does not change, i.e.
n
–
1 =
c
ρ
for
some constant
c
[4]. Assume the gas obeys the ideal gas law,
m
PV
=
RT
M
where
V
is the volume,
m
and
M
the total and the molar masses, respectively,
R
is the
universal gas constant and T is the absolute temperature. We will rewrite it in the form
1
t
Mf
dP
dn
l
dP
dN
2